SketchWave Bell Curve Demo

What is a Bell Curve?

A bell curve (also called a Gaussian curve or normal distribution) is the most famous curve in statistics. It describes how many natural measurements — heights, test scores, measurement errors — cluster around a central value and taper off symmetrically on both sides. Its characteristic bell shape comes from the exponential decay function below.

The Formula

y = A · exp( −x² / (2σ²) )

  A = amplitude  — peak height from baseline to tip (pixels)
  σ = sigma     — standard deviation; controls width (pixels)
  x = distance from the centre line

At x = 0 the curve reaches its maximum (y = A). As |x| grows the curve falls exponentially toward zero. SWBellCurve draws the closed shape formed by the arc plus a flat baseline.

Key Measurements

Property	Formula	Meaning
fwhm	2σ√(2 ln 2) ≈ 2.355σ	Full Width at Half Maximum — width of the curve where it reaches half its peak height
totalWidth	2 × σ × tailRange	Drawn width of the shape (default tail range = 3.5σ, capturing >99.9% of the curve)
area	A × σ × √(2π)	Approximate area under the curve (infinite-integral estimate)

Positioning

cx, cy is the bounding-box centre. The peak rises amplitude/2 above the centre line; the flat baseline sits amplitude/2 below. Drag the shape to reposition it.

Constructor

new SWBellCurve(cx, cy, amplitude, sigma, fillColor, options)

Option	Type	Default	Description
strokeColor	SWColor | null	null	Outline colour; null = no stroke
strokeWeight	number	2	Stroke width in pixels
drawRangeFactor	number	3.5	How many σ to draw on each side (min 1)
resolution	number	120	Number of sample points along the arc

Breathing Modes

• Both — breathe(sinusoid, t): amplitude and sigma scale together. The curve grows and shrinks uniformly.
• Vertical — breatheVertical(sinusoid, t): only amplitude scales. The bell gets taller and shorter while keeping the same width.
• Horizontal — breatheHorizontal(sinusoid, t): only sigma scales. The bell gets wider and narrower while keeping the same peak height.

Using the Controls

• Amplitude / Sigma / Tail Range: Sliders above the accordion set the shape dimensions.
• Rotation Angle: Sets a static pose. Use Spinning for continuous rotation.
• Breathing Mode: Choose Both, Vertical, or Horizontal before turning breathing on.
• Drag: Click and drag the shape to reposition it on the canvas.

Keyboard Shortcuts

• B — toggle breathing
• S — toggle spin
• R — factory reset
• Q — quit all animations